Details

sample285.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	172×	body	80	valid
6.0ms	34×	body	1280	valid
3.0ms	88×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5001	2063

prune609.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b	(- (* b_2 b_2) (* a c))
6.2b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 889

Calls

4 calls:

16.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
8.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify259.0ms

Algorithm

egg-herbie

Counts

901 → 901

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1958	39816
1	5001	25884

prune5.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(- (* b_2 b_2) (* a c))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 59

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
11.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt a)
173.0ms	(cbrt a)
32.0ms	(- (* b_2 b_2) (* a c))
51.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	195	306
1	589	286
2	2053	277
3	5001	272

prune432.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
10.7b	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
69×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`add-cube-cbrt`
35×	`fma-neg` `prod-diff`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`add-exp-log` `associate-r`
10×	`sqrt-div`
9×	`sqrt-prod` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `flip3--` `flip--`
6×	`neg-mul-1` `associate-l` `frac-sub` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `prod-exp` `log1p-expm1-u` `div-inv`
3×	`associate-*r/` `un-div-inv`
2×	`sub-neg` `diff-log` `div-exp` `cbrt-unprod` `sub-div`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `distribute-rgt-out--` `sqrt-pow1` `pow1/2` `1-exp` `div-sub` `pow-prod-down` `*-commutative`

Counts

4 → 173

Calls

4 calls:

35.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
10.0ms	(- (* b_2 b_2) (* a c))
54.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
29.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	752	2220
1	2748	1911
2	5002	1871

prune846.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.9b

regimes423.0ms

Accuracy

85.9% (4.0b remaining)

Error of 9.6b against oracle of 5.5b and baseline of 34.2b

bsearch75.0ms

Steps

Iters	Range		Point
7	4.552856064668592e+138	1.6396378931841617e+140	9.068455564205939e+138
4	-9.285856612195885e-64	-5.291128096587059e-64	-5.365827530591872e-64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	17
1	29	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

240.0ms	1086×	body	2560	valid
235.0ms	5862×	body	80	valid
167.0ms	897×	body	1280	valid
110.0ms	3042×	body	80	nan
68.0ms	468×	body	640	valid
29.0ms	108×	body	5120	valid
21.0ms	197×	body	320	valid
8.0ms	112×	body	160	valid